mirror of
https://github.com/roc-lang/roc.git
synced 2025-09-30 07:14:46 +00:00
Merge pull request #550 from rtfeldman/regenerate-builtin-bitcode
Regenerate builtin bitcode via regenerate.sh
This commit is contained in:
commit
5dc1dace68
6 changed files with 233 additions and 210 deletions
3
.github/workflows/ci.yml
vendored
3
.github/workflows/ci.yml
vendored
|
@ -9,6 +9,9 @@ jobs:
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||||||
steps:
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steps:
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- uses: actions/checkout@v1
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- uses: actions/checkout@v1
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||||||
|
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- name: Verify compiler/builtin/bitcode/regenerate.sh was run if necessary
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run: pushd compiler/builtins/bitcode && ./regenerate.sh && git diff --exit-code ../../gen/src/llvm/builtins.bc && popd
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|
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- name: Install LLVM
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- name: Install LLVM
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run: sudo ./ci/install-llvm.sh 10
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run: sudo ./ci/install-llvm.sh 10
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|
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|
|
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@ -17,42 +17,37 @@ The source we'll use to generate the bitcode is in `src/lib.rs` in this director
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To generate the bitcode, `cd` into `compiler/builtins/bitcode/` and run:
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To generate the bitcode, `cd` into `compiler/builtins/bitcode/` and run:
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```bash
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```bash
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$ cargo rustc --release --lib -- --emit=llvm-bc
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$ ./regenerate.sh
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```
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```
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Then look in the root `roc` source directory under `target/release/deps/` for a file
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with a name like `roc_builtins_bitcode-8da0901c58a73ebf.bc` - except
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probably with a different hash before the `.bc`. If there's more than one
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`*.bc` file in that directory, delete the whole `deps/` directory and re-run
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the `cargo rustc` command above to regenerate it.
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> If you want to take a look at the human-readable LLVM IR rather than the
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> If you want to take a look at the human-readable LLVM IR rather than the
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> bitcode, run this instead and look for a `.ll` file instead of a `.bc` file:
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> bitcode, run this instead and look for a `.ll` file instead of a `.bc` file:
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>
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>
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> ```bash
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> ```bash
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> $ cargo rustc --release --lib -- --emit=llvm-ir
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> $ cargo rustc --release --lib -- --emit=llvm-ir
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> ```
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> ```
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>
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> Then look in the root `roc` source directory under `target/release/deps/` for a file
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> with a name like `roc_builtins_bitcode-8da0901c58a73ebf.bc` - except
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> probably with a different hash before the `.bc`. If there's more than one
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> `*.bc` file in that directory, delete the whole `deps/` directory and re-run
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> the `cargo rustc` command above to regenerate it.
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**Note**: In order to be able to address the bitcode functions by name, they need to be defined with the `#[no_mangle]` attribute.
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**Note**: In order to be able to address the bitcode functions by name, they need to be defined with the `#[no_mangle]` attribute.
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## Importing the bitcode
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The bitcode is a bunch of bytes that aren't particularly human-readable.
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The bitcode is a bunch of bytes that aren't particularly human-readable.
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Since Roc is designed to be distributed as a single binary, these bytes
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Since Roc is designed to be distributed as a single binary, these bytes
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need to be included in the raw source somewhere.
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need to be included in the raw source somewhere.
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The `llvm/src/build.rs` file statically imports these raw bytes
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The `llvm/src/build.rs` file statically imports these raw bytes
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using the [`include_bytes!` macro](https://doc.rust-lang.org/std/macro.include_bytes.html),
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using the [`include_bytes!` macro](https://doc.rust-lang.org/std/macro.include_bytes.html).
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so we just need to move the `.bc` file from the previous step to the correct
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location.
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The current `.bc` file is located at:
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The current `.bc` file is located at:
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|
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```
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```
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compiler/gen/src/llvm/builtins.bc
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compiler/gen/src/llvm/builtins.bc
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```
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```
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|
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...so you want to overwrite it with the new `.bc` file in `target/deps/`
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The script will automatically replace this `.bc` file with the new one.
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|
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Once that's done, `git status` should show that the `builtins.bc` file
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Once that's done, `git status` should show that the `builtins.bc` file
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has been changed. Commit that change and you're done!
|
has been changed. Commit that change and you're done!
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19
compiler/builtins/bitcode/regenerate.sh
Executable file
19
compiler/builtins/bitcode/regenerate.sh
Executable file
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@ -0,0 +1,19 @@
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#!/bin/bash
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set -euxo pipefail
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# Clear out any existing output files. Sometimes if these are there, rustc
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# doesn't generate the .bc file - or we can end up with more than one .bc
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rm -rf ../../../target/release/deps/
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# Regenerate the .bc file
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cargo rustc --release --lib -- --emit=llvm-bc
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bc_files=$(ls ../../../target/release/deps/*.bc | wc -l)
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if [[ $bc_files != 1 ]]; then
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echo "More than one .bc file was emitted somehow."
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exit 1;
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fi
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cp ../../../target/release/deps/*.bc ../../gen/src/llvm/builtins.bc
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@ -4,6 +4,8 @@
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#![crate_type = "lib"]
|
#![crate_type = "lib"]
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#![no_std]
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#![no_std]
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|
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mod libm;
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|
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/// TODO replace this with a normal Inkwell build_cast call - this was just
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/// TODO replace this with a normal Inkwell build_cast call - this was just
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/// used as a proof of concept for getting bitcode importing working!
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/// used as a proof of concept for getting bitcode importing working!
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#[no_mangle]
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#[no_mangle]
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|
@ -46,202 +48,7 @@ pub fn is_finite_(num: f64) -> bool {
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f64::is_finite(num)
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f64::is_finite(num)
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}
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}
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|
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/// Adapted from Rust's libm module, by the Rust core team,
|
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/// licensed under the Apache License, version 2.0 - https://www.apache.org/licenses/LICENSE-2.0
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/// https://github.com/rust-lang/libm/blob/master/LICENSE-APACHE
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///
|
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||||||
/// Thank you, Rust core team!
|
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|
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||||||
// From https://github.com/rust-lang/libm/blob/master/src/math/mod.rs
|
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#[cfg(not(debug_assertions))]
|
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macro_rules! i {
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($array:expr, $index:expr) => {
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unsafe { *$array.get_unchecked($index) }
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};
|
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($array:expr, $index:expr, = , $rhs:expr) => {
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unsafe {
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*$array.get_unchecked_mut($index) = $rhs;
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}
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};
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($array:expr, $index:expr, += , $rhs:expr) => {
|
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unsafe {
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*$array.get_unchecked_mut($index) += $rhs;
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||||||
}
|
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||||||
};
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($array:expr, $index:expr, -= , $rhs:expr) => {
|
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unsafe {
|
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*$array.get_unchecked_mut($index) -= $rhs;
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||||||
}
|
|
||||||
};
|
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($array:expr, $index:expr, &= , $rhs:expr) => {
|
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||||||
unsafe {
|
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*$array.get_unchecked_mut($index) &= $rhs;
|
|
||||||
}
|
|
||||||
};
|
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||||||
($array:expr, $index:expr, == , $rhs:expr) => {
|
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||||||
unsafe { *$array.get_unchecked_mut($index) == $rhs }
|
|
||||||
};
|
|
||||||
}
|
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||||||
|
|
||||||
#[cfg(debug_assertions)]
|
|
||||||
macro_rules! i {
|
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||||||
($array:expr, $index:expr) => {
|
|
||||||
*$array.get($index).unwrap()
|
|
||||||
};
|
|
||||||
($array:expr, $index:expr, = , $rhs:expr) => {
|
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||||||
*$array.get_mut($index).unwrap() = $rhs;
|
|
||||||
};
|
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||||||
($array:expr, $index:expr, -= , $rhs:expr) => {
|
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*$array.get_mut($index).unwrap() -= $rhs;
|
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||||||
};
|
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($array:expr, $index:expr, += , $rhs:expr) => {
|
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*$array.get_mut($index).unwrap() += $rhs;
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|
||||||
};
|
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($array:expr, $index:expr, &= , $rhs:expr) => {
|
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*$array.get_mut($index).unwrap() &= $rhs;
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|
||||||
};
|
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||||||
($array:expr, $index:expr, == , $rhs:expr) => {
|
|
||||||
*$array.get_mut($index).unwrap() == $rhs
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|
||||||
};
|
|
||||||
}
|
|
||||||
|
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||||||
macro_rules! llvm_intrinsically_optimized {
|
|
||||||
(#[cfg($($clause:tt)*)] $e:expr) => {
|
|
||||||
#[cfg(all(feature = "unstable", $($clause)*))]
|
|
||||||
{
|
|
||||||
if true { // thwart the dead code lint
|
|
||||||
$e
|
|
||||||
}
|
|
||||||
}
|
|
||||||
};
|
|
||||||
}
|
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||||||
|
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macro_rules! force_eval {
|
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||||||
($e:expr) => {
|
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||||||
unsafe {
|
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||||||
::core::ptr::read_volatile(&$e);
|
|
||||||
}
|
|
||||||
};
|
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||||||
}
|
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||||||
|
|
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// From https://github.com/rust-lang/libm/blob/master/src/math/atan.rs
|
|
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|
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// Clippy fails CI if we don't include overrides below. Since this is copied
|
|
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// straight from the libm crate, I figure they had a reason to include
|
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||||||
// the extra percision, so we just silence this warning.
|
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|
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#[allow(clippy::excessive_precision)]
|
|
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const ATANHI: [f64; 4] = [
|
|
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4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
|
||||||
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
|
||||||
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
|
||||||
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
|
||||||
];
|
|
||||||
|
|
||||||
#[allow(clippy::excessive_precision)]
|
|
||||||
const ATANLO: [f64; 4] = [
|
|
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2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
|
||||||
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
|
||||||
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
|
||||||
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
|
||||||
];
|
|
||||||
|
|
||||||
#[allow(clippy::excessive_precision)]
|
|
||||||
const AT: [f64; 11] = [
|
|
||||||
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
|
||||||
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
|
||||||
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
|
||||||
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
|
||||||
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
|
||||||
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
|
||||||
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
|
||||||
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
|
||||||
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
|
||||||
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
|
||||||
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
|
||||||
];
|
|
||||||
|
|
||||||
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
|
|
||||||
pub fn fabs(x: f64) -> f64 {
|
|
||||||
// On wasm32 we know that LLVM's intrinsic will compile to an optimized
|
|
||||||
// `f64.abs` native instruction, so we can leverage this for both code size
|
|
||||||
// and speed.
|
|
||||||
llvm_intrinsically_optimized! {
|
|
||||||
#[cfg(target_arch = "wasm32")] {
|
|
||||||
return unsafe { ::core::intrinsics::fabsf64(x) }
|
|
||||||
}
|
|
||||||
}
|
|
||||||
f64::from_bits(x.to_bits() & (u64::MAX / 2))
|
|
||||||
}
|
|
||||||
|
|
||||||
#[no_mangle]
|
#[no_mangle]
|
||||||
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
|
|
||||||
pub fn atan_(x: f64) -> f64 {
|
pub fn atan_(x: f64) -> f64 {
|
||||||
let mut x = x;
|
libm::atan(x)
|
||||||
let mut ix = (x.to_bits() >> 32) as u32;
|
|
||||||
let sign = ix >> 31;
|
|
||||||
ix &= 0x7fff_ffff;
|
|
||||||
if ix >= 0x4410_0000 {
|
|
||||||
if x.is_nan() {
|
|
||||||
return x;
|
|
||||||
}
|
|
||||||
|
|
||||||
let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
|
|
||||||
return if sign != 0 { -z } else { z };
|
|
||||||
}
|
|
||||||
|
|
||||||
let id = if ix < 0x3fdc_0000 {
|
|
||||||
/* |x| < 0.4375 */
|
|
||||||
if ix < 0x3e40_0000 {
|
|
||||||
/* |x| < 2^-27 */
|
|
||||||
if ix < 0x0010_0000 {
|
|
||||||
/* raise underflow for subnormal x */
|
|
||||||
force_eval!(x as f32);
|
|
||||||
}
|
|
||||||
|
|
||||||
return x;
|
|
||||||
}
|
|
||||||
|
|
||||||
-1
|
|
||||||
} else {
|
|
||||||
x = fabs(x);
|
|
||||||
if ix < 0x3ff30000 {
|
|
||||||
/* |x| < 1.1875 */
|
|
||||||
if ix < 0x3fe60000 {
|
|
||||||
/* 7/16 <= |x| < 11/16 */
|
|
||||||
x = (2. * x - 1.) / (2. + x);
|
|
||||||
0
|
|
||||||
} else {
|
|
||||||
/* 11/16 <= |x| < 19/16 */
|
|
||||||
x = (x - 1.) / (x + 1.);
|
|
||||||
1
|
|
||||||
}
|
|
||||||
} else if ix < 0x40038000 {
|
|
||||||
/* |x| < 2.4375 */
|
|
||||||
x = (x - 1.5) / (1. + 1.5 * x);
|
|
||||||
2
|
|
||||||
} else {
|
|
||||||
/* 2.4375 <= |x| < 2^66 */
|
|
||||||
x = -1. / x;
|
|
||||||
3
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
let z = x * x;
|
|
||||||
let w = z * z;
|
|
||||||
/* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
|
|
||||||
let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
|
|
||||||
let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
|
|
||||||
|
|
||||||
if id < 0 {
|
|
||||||
return x - x * (s1 + s2);
|
|
||||||
}
|
|
||||||
|
|
||||||
let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);
|
|
||||||
|
|
||||||
if sign != 0 {
|
|
||||||
-z
|
|
||||||
} else {
|
|
||||||
z
|
|
||||||
}
|
|
||||||
}
|
}
|
||||||
|
|
199
compiler/builtins/bitcode/src/libm.rs
Normal file
199
compiler/builtins/bitcode/src/libm.rs
Normal file
|
@ -0,0 +1,199 @@
|
||||||
|
/// Adapted from Rust's libm module, by the Rust core team,
|
||||||
|
/// licensed under the Apache License, version 2.0 - https://www.apache.org/licenses/LICENSE-2.0
|
||||||
|
/// https://github.com/rust-lang/libm/blob/master/LICENSE-APACHE
|
||||||
|
///
|
||||||
|
/// Thank you, Rust core team!
|
||||||
|
|
||||||
|
// From https://github.com/rust-lang/libm/blob/master/src/math/mod.rs
|
||||||
|
#[cfg(not(debug_assertions))]
|
||||||
|
macro_rules! i {
|
||||||
|
($array:expr, $index:expr) => {
|
||||||
|
unsafe { *$array.get_unchecked($index) }
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, = , $rhs:expr) => {
|
||||||
|
unsafe {
|
||||||
|
*$array.get_unchecked_mut($index) = $rhs;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, += , $rhs:expr) => {
|
||||||
|
unsafe {
|
||||||
|
*$array.get_unchecked_mut($index) += $rhs;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, -= , $rhs:expr) => {
|
||||||
|
unsafe {
|
||||||
|
*$array.get_unchecked_mut($index) -= $rhs;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, &= , $rhs:expr) => {
|
||||||
|
unsafe {
|
||||||
|
*$array.get_unchecked_mut($index) &= $rhs;
|
||||||
|
}
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, == , $rhs:expr) => {
|
||||||
|
unsafe { *$array.get_unchecked_mut($index) == $rhs }
|
||||||
|
};
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(debug_assertions)]
|
||||||
|
macro_rules! i {
|
||||||
|
($array:expr, $index:expr) => {
|
||||||
|
*$array.get($index).unwrap()
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, = , $rhs:expr) => {
|
||||||
|
*$array.get_mut($index).unwrap() = $rhs;
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, -= , $rhs:expr) => {
|
||||||
|
*$array.get_mut($index).unwrap() -= $rhs;
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, += , $rhs:expr) => {
|
||||||
|
*$array.get_mut($index).unwrap() += $rhs;
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, &= , $rhs:expr) => {
|
||||||
|
*$array.get_mut($index).unwrap() &= $rhs;
|
||||||
|
};
|
||||||
|
($array:expr, $index:expr, == , $rhs:expr) => {
|
||||||
|
*$array.get_mut($index).unwrap() == $rhs
|
||||||
|
};
|
||||||
|
}
|
||||||
|
|
||||||
|
macro_rules! llvm_intrinsically_optimized {
|
||||||
|
(#[cfg($($clause:tt)*)] $e:expr) => {
|
||||||
|
#[cfg(all(feature = "unstable", $($clause)*))]
|
||||||
|
{
|
||||||
|
if true { // thwart the dead code lint
|
||||||
|
$e
|
||||||
|
}
|
||||||
|
}
|
||||||
|
};
|
||||||
|
}
|
||||||
|
|
||||||
|
macro_rules! force_eval {
|
||||||
|
($e:expr) => {
|
||||||
|
unsafe {
|
||||||
|
::core::ptr::read_volatile(&$e);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
}
|
||||||
|
|
||||||
|
// From https://github.com/rust-lang/libm/blob/master/src/math/atan.rs
|
||||||
|
|
||||||
|
// Clippy fails CI if we don't include overrides below. Since this is copied
|
||||||
|
// straight from the libm crate, I figure they had a reason to include
|
||||||
|
// the extra percision, so we just silence this warning.
|
||||||
|
|
||||||
|
#[allow(clippy::excessive_precision)]
|
||||||
|
const ATANHI: [f64; 4] = [
|
||||||
|
4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */
|
||||||
|
7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */
|
||||||
|
9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */
|
||||||
|
1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */
|
||||||
|
];
|
||||||
|
|
||||||
|
#[allow(clippy::excessive_precision)]
|
||||||
|
const ATANLO: [f64; 4] = [
|
||||||
|
2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */
|
||||||
|
3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */
|
||||||
|
1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */
|
||||||
|
6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */
|
||||||
|
];
|
||||||
|
|
||||||
|
#[allow(clippy::excessive_precision)]
|
||||||
|
const AT: [f64; 11] = [
|
||||||
|
3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */
|
||||||
|
-1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */
|
||||||
|
1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */
|
||||||
|
-1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */
|
||||||
|
9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */
|
||||||
|
-7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */
|
||||||
|
6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */
|
||||||
|
-5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */
|
||||||
|
4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */
|
||||||
|
-3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */
|
||||||
|
1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */
|
||||||
|
];
|
||||||
|
|
||||||
|
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
|
||||||
|
pub fn fabs(x: f64) -> f64 {
|
||||||
|
// On wasm32 we know that LLVM's intrinsic will compile to an optimized
|
||||||
|
// `f64.abs` native instruction, so we can leverage this for both code size
|
||||||
|
// and speed.
|
||||||
|
llvm_intrinsically_optimized! {
|
||||||
|
#[cfg(target_arch = "wasm32")] {
|
||||||
|
return unsafe { ::core::intrinsics::fabsf64(x) }
|
||||||
|
}
|
||||||
|
}
|
||||||
|
f64::from_bits(x.to_bits() & (u64::MAX / 2))
|
||||||
|
}
|
||||||
|
|
||||||
|
#[inline(always)]
|
||||||
|
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
|
||||||
|
pub fn atan(x: f64) -> f64 {
|
||||||
|
let mut x = x;
|
||||||
|
let mut ix = (x.to_bits() >> 32) as u32;
|
||||||
|
let sign = ix >> 31;
|
||||||
|
ix &= 0x7fff_ffff;
|
||||||
|
if ix >= 0x4410_0000 {
|
||||||
|
if x.is_nan() {
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
|
||||||
|
let z = ATANHI[3] + f64::from_bits(0x0380_0000); // 0x1p-120f
|
||||||
|
return if sign != 0 { -z } else { z };
|
||||||
|
}
|
||||||
|
|
||||||
|
let id = if ix < 0x3fdc_0000 {
|
||||||
|
/* |x| < 0.4375 */
|
||||||
|
if ix < 0x3e40_0000 {
|
||||||
|
/* |x| < 2^-27 */
|
||||||
|
if ix < 0x0010_0000 {
|
||||||
|
/* raise underflow for subnormal x */
|
||||||
|
force_eval!(x as f32);
|
||||||
|
}
|
||||||
|
|
||||||
|
return x;
|
||||||
|
}
|
||||||
|
|
||||||
|
-1
|
||||||
|
} else {
|
||||||
|
x = fabs(x);
|
||||||
|
if ix < 0x3ff30000 {
|
||||||
|
/* |x| < 1.1875 */
|
||||||
|
if ix < 0x3fe60000 {
|
||||||
|
/* 7/16 <= |x| < 11/16 */
|
||||||
|
x = (2. * x - 1.) / (2. + x);
|
||||||
|
0
|
||||||
|
} else {
|
||||||
|
/* 11/16 <= |x| < 19/16 */
|
||||||
|
x = (x - 1.) / (x + 1.);
|
||||||
|
1
|
||||||
|
}
|
||||||
|
} else if ix < 0x40038000 {
|
||||||
|
/* |x| < 2.4375 */
|
||||||
|
x = (x - 1.5) / (1. + 1.5 * x);
|
||||||
|
2
|
||||||
|
} else {
|
||||||
|
/* 2.4375 <= |x| < 2^66 */
|
||||||
|
x = -1. / x;
|
||||||
|
3
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
let z = x * x;
|
||||||
|
let w = z * z;
|
||||||
|
/* break sum from i=0 to 10 AT[i]z**(i+1) into odd and even poly */
|
||||||
|
let s1 = z * (AT[0] + w * (AT[2] + w * (AT[4] + w * (AT[6] + w * (AT[8] + w * AT[10])))));
|
||||||
|
let s2 = w * (AT[1] + w * (AT[3] + w * (AT[5] + w * (AT[7] + w * AT[9]))));
|
||||||
|
|
||||||
|
if id < 0 {
|
||||||
|
return x - x * (s1 + s2);
|
||||||
|
}
|
||||||
|
|
||||||
|
let z = i!(ATANHI, id as usize) - (x * (s1 + s2) - i!(ATANLO, id as usize) - x);
|
||||||
|
|
||||||
|
if sign != 0 {
|
||||||
|
-z
|
||||||
|
} else {
|
||||||
|
z
|
||||||
|
}
|
||||||
|
}
|
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Loading…
Add table
Add a link
Reference in a new issue